package dp01;

/**
 * 题目：最小路径和
 * 题目链接：https://leetcode.cn/problems/minimum-path-sum/
 */
public class Solution5 {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m+1][n+1];
        //初始化值，防止填dp表出错
        for (int i = 0; i <= n ; i++) {       //初始化行
            dp[0][i] = Integer.MAX_VALUE;
        }
        for (int i = 0; i <= m ; i++) {      //初始化列
            dp[i][0] = Integer.MAX_VALUE;
        }
        dp[0][1] = dp[1][0] = 0;    //保证dp[1][1]为原值
        //开始填表
        for (int i = 1; i <= m ; i++) {
            for (int j = 1; j <= n ; j++) {
                dp[i][j] = Math.min(dp[i-1][j],dp[i][j-1]) + grid[i-1][j-1];
            }
        }
        return dp[m][n];
    }
}
